"Constructing Triangles with Rulers and Compasses" Triangle PPT Courseware

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"Constructing Triangles with Rulers and Compasses" Triangle PPT Courseware

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The triangle in Doudou's book was partially stained by ink stains. He wanted to draw a triangle on his homework book that was exactly the same as the one in the book. What should he do?

Looking back

The basic elements of a triangle are __________ and __________.

Can you use a ruler and compass to draw a line segment equal to a known line segment?

Try it yourself!

Can you use a ruler and compass to find an angle equal to a known angle?

Can you use a ruler and compass to construct a triangle that is congruent to a known triangle?

Practice brings true knowledge

1. Given the two angles of a triangle and the included side, find the triangle.

Known: ∠α, ∠β, line segment c.

Find: △ABC, let ∠A=∠α, ∠B=∠β, AB=c.

2. Given the two sides and included angles of a triangle, find the triangle.

Known: line segments a, c, ∠α.

Find: △ABC, let BC=a, AB=c, ∠ABC=∠α.

After the previous practice, how do we analyze the drawing questions?

1. Assume that the required graphics have been made and a sketch is made on the draft paper;

2. Mark the corresponding positions of the given sides and angles on the sketch;

3. First find the basic graphics from the sketch, and thereby determine the starting steps for drawing;

4. On the basis of 3, gradually expand to the desired shape.

Let's do it together!

1. Can you use a ruler and compass to construct a right triangle so that its two right-angled sides are equal to the known line segments a and b respectively? And write down the practice.

Analysis: First draw a hypothetical "triangle that has been made" on the scratch paper. You will find that "the two sides and the included angle are known to find the triangle", so follow this method to draw.

2. Given ∠α and ∠β and line segment a, use a ruler and compass to construct a triangle so that one interior angle is equal to ∠α, the other interior angle is equal to ∠β, and the opposite side of ∠α is equal to a.

Tip: First make an angle equal to ∠α+∠β, and then extend one side of the angle in reverse to get its supplementary angle, which is the third interior angle ∠ γ in the triangle. This is converted into known ∠β and ∠γ and the side a included by these two angles, and the triangle is found.

Expand and improve

Given the line segments a, b and ∠α, find △ABC so that it has one interior angle equal to ∠α, and the opposite side of ∠α is equal to a, and the other side is equal to b.

Analysis: First draw a hypothetical "made triangle" on the scratch paper; then mark the corresponding positions of the given sides and angles on the sketch; then find the sides and angles and determine the order of drawing.

Given the same two sides and one angle, why do two triangles appear?

What can you learn from it?

practice:

1. Make ∠MAN=∠α

2. Intercept AB=b on ray AM

3. With B as the center and a as the radius, draw an arc and intersect AN at point C, C'

4. Connect BC, BC' △ABC and △ABC' to be the triangle you want to construct.

Insight: Knowing both sides and one corner of a triangle does not necessarily determine only one triangle. When two sides and the angle between them are known, a triangle can be determined, so it can be used to determine that two triangles are congruent; but when two sides and the opposite angle of one side are known, two different triangles will be drawn, so it cannot be used as a Determine the conditions for two triangles to be congruent.

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For more information about the PPT courseware "Using a Ruler and Compass to Construct Triangles from a Triangle", please click the Triangle ppt Constructing a Triangle with a Ruler and Compasses ppt tag.

"Constructing Triangles with Rulers and Compasses" Triangle PPT Courseware 3:

"Constructing Triangles with Rulers and Compasses" Triangle PPT Courseware 3 Do it 1. Given the two sides of a triangle and the angle between them, find the triangle. Known: line segment a c. Find: △ABC, so that BC=a AB=c ABC=. 2. Given the two angles of the triangle and the included side, find this...

"Constructing Triangles with Rulers and Compasses" Triangle PPT Courseware 2:

"Constructing Triangles with Rulers and Compasses" Triangle PPT Courseware 2 Do it. Can you make a triangle according to the conditions on page 147 of the book? Cut out the triangles you made and compare them with your partner to see if they are congruent? Can you give a reason why they are equal? Both sides and their included angles are equal.

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Update Time: 2024-11-12

This template belongs to Mathematics courseware Beijing Normal University seventh grade mathematics volume 2 industry PPT template

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